1 The story is all over the place, too many plotlines make for a terribly confusing movie, especially when the time is limited to 2 hours max.
2 good child actors are few and finding ones that look similar enough to represent the next generation in each year is practically impossible (also too many time jumps, don't work well in movies either)
3 CC forgets everything we learned about the old characters and pushes them into stereotypes that don't fit whatsoever (e.g. Harry being a miserable absent dad etc.)
4 It also doesn't line up with the established logic of the hp series (time turner technology, Bellatrixs' pregnancy etc.)
5 It might work in theatre (I don't know it's far too expensive and far away for me to see it) but film is a very different medium, just look at what they did to Cats or Phantom of the opera